9 Consider the following demand scenario: Quantity Probability 2000 3% 2100 8% 2200 15% 2300 30% 2400 17% 2500 12% 2600 10% 2700 5% Suppose the manufacturer produces at a cost of $20/unit. The distributor sells to the end customers for $50/unit during season, unsold units are sold for $10/unit after season. A. What is the system optimal production quantity and expected profit under global optimization? B. Suppose the manufacturer is make-to-order; that is, the timing of events is as follows; The distributor orders before it receives demand from end customers. The manufacturer produces the amount ordered by the distributor. Customer demand is observed. i. Suppose the manufacturer sells to the distributor at $40/unit, how much will the distributor order? What is the expected profit for the manufacturer and the distributor? ii. Find an option contract such that both the manufacturer and distributor enjoy a higher expected profit than (b)(i). What is the expected profit for the manufacturer and the distributor? C. Suppose the manufacturer is make-to-stock; that is, the timing of events is as follows: The manufacturer produces a certain amount. The distributor observes demand. The distributor orders from the manufacturer. I. Using the same wholesale price contract as part (b)(i), calculate the production/inventory level of the manufacturer. What is the expected profit for the manufacturer and the distributor? Compare your results with part (b)(i). II. Find a cost-sharing contract such that both the manufacturer and the distributor enjoy a higher expected profit than that in (c)(i), and calculate their expected profits. Problem 10 Using the data of Question 9, suppose the manufacturer has an inflated demand forecast as follows: Quantity Probability 2200 5% 2300 6% 2400 10% 2500 17% 2600 30% 2700 17% 2800 12% 2900 3% A. Suppose the manufacturer is make-to-order (timing of events as in 9(b)). Using your contract in Question 9(b)(ii), find the order quantity, and expected profits of the distributor and the manufacturer. Compare your answers with 9(b)(ii). B. Suppose the manufacturer is make0to0stock (timing of events as in 9(c)). Using your contract in Question 9(c)(ii), find the production quantity, expected profits of the manufacturer and of the distributor. Compare your answers with 9(c)(ii). C. If you are the distributor and you have the choice of revealing the true demand forecast or inflated demand forecast to the manufacturer, what will you do in each case? Explain